数学杂志2023，Vol.43Issue(5)：398-408,11.
二维Hardy空间维林肯型系统的极大算子
TWO-DIMENSIONAL MAXIMAL OPERATOR OF VILENKIN-LIKE SYSTEM ON HARDY SPACES
摘要
Abstract
In this paper,we research the boundedness of two-dimensional maximal operator of Vilenkin-like system on Hardy spaces.By means of atomic decomposition,the two-dimensional maximal operator Tαf:=sup2-α≤n/m≤2α|f*Pn,m| is bounded from Hp to Lp,where 0＜p＜1/2 and α ≥ 0.As an application,we prove the boundedness of two-dimensional operator(σ)*f=sup2-α≤n/m≤2α|σn,mf|/[(n+1)(m+1)]1/p-2.By a counterexample,we also prove that two dimensional maximal operator(σ)*f=sup n,m∈N |σn,mf|/[(n+1)(m+1)]1/2p-1.is not bounded from Hp to Lp,where 0＜p＜1/2.The results as above generalize the known conclusions in Walsh system or in Vilenkin system.关键词
维林肯型系统/极大算子/Dirichlet核/Fejér核Key words
Vilenkin-like system/maximal operator/Dirichlet kernels/Fejér kernels分类
数理科学引用本文复制引用
张学英,王超越,张传洲,肖俊..二维Hardy空间维林肯型系统的极大算子[J].数学杂志,2023,43(5):398-408,11.基金项目
Supported by National Natural Science Foundation of China(11871195). （11871195）
